The invention relates to a method and apparatus for reducing peak-to-average power ratio in telecommunications systems.
Multi-Carrier (MC) modulation techniques [1] and in particular Orthogonal Frequency Division Multiplexing (OFDM) [1] constitute efficient modulation schemes, which are suitable for wireless broadband communications. In recent years several industrial standards based on OFDM have emerged, such as the Terrestrial Digital Video Broadcast (DVB-T), the IEEE 802.11 Wireless Local Area Network (W-LAN) scheme, as well as the IEEE 802.16 Broadband Wireless Access (BWA) standard. The more extensive employment of these systems is limited by their relatively high implementation cost, which is a consequence of requiring high-linearity, Class A amplifiers having a low power-efficiency. This requirement is imposed by the high Peak-to-Average Power Ratio (PAPR) of the OFDM signal, potentially resulting in non-linear distortions producing upper harmonics of the signal and associated out-of-band emissions [2,3]. The most problematic non-linear component within the transmission chain is the Power Amplifier (PA).
The most straightforward method of improving the linearity of the PA is to use an amplifier ‘back-off’, implying that the PA is configured to operate at a certain power, which provides a sufficiently high head-room for the high modulated signal peaks to be amplified without clipping. This allows the entire input signal to be amplified within the PA's linear range. Back-off results in inefficient operation of the PA. In some systems the power back-off requirements are as high as 12 dB. In terms of system costs, this translates into requiring a more than 10 times more powerful PA, which may be significantly more expensive. Therefore, the only attractive solution for improving the cost efficiency of MC systems is the reduction of the PAPR of the signal.
The PAPR properties of MC signals are now discussed. The non-linear distortion effects imposed by the PA manifest themselves as a reduction of the signal amplitude peaks according to the PA's Amplitude-to-Amplitude (AM/AM) conversion characteristic. A typical AM/AM transfer characteristic can be seen in FIG. 1. The intercept point in the figure indicates the so-called 1 dB compression point, where the output power level is 1 dB below the expected linear transfer function as a consequence of the compression of high output signal peaks.
The power of the distortion products produced by the PA is often defined as the amount of signal energy fed into the PA in excess of that corresponding to the 1 dB compression point. This quantity may be further characterized by the Peak-to-Average Power Ratio (PAPR) properties, i.e. by quantifying the statistical deviation of the input signal power peaks from the Root Mean Square (RMS) power. The signal's PAPR properties can also by characterized by the Threshold Crossing Probability (TCP), i.e. by the probability that the signal amplitude exceeds a certain threshold level. The TCP plot recorded for several single carrier modulation schemes and for a 1024-subcarrier OFDM scheme is depicted in FIG. 2.
In case of OFDM the transmitted baseband signal may be represented as:
                                          s            ⁡                          (              t              )                                =                                    ∑                              k                =                0                                            K                -                1                                      ⁢                                                  ⁢                                          (                                                      a                    k                                    +                                      j                    ⁢                                                                                  ⁢                                          b                      k                                                                      )                            ⁢                              exp                ⁡                                  (                                                            -                      j                                        ⁢                                                                                  ⁢                    2                    ⁢                                                                                  ⁢                                          πω                      k                                        ⁢                    t                                    )                                                                    ,                            (        1        )            
where K is the number of subcarriers, while ak and bk are the real and imaginary components of the complex modulating symbols of the K subcarriers, respectively. For example, for 16-QAM modulation ak and bk may assume the equiprobable values of {−3, −1, 1, 3}. From the central limit theorem it follows [8] that for large values of K (in practice for K exceeding 64), both the real and imaginary component of s(t) become normally distributed variables having a mean of zero. Hence the amplitude of the complex baseband OFDM signal (for K>64) is complex Gaussian, or—synonymously—Rayleigh distributed. The distribution of the instantaneous power level hence becomes a central chi-square distribution with two degrees of freedom. In tangible physically interpreted terms the high PAPR is a consequence of the constructive superposition of high subcarrier values of numerous subcarriers.
Numerous studies have been published in recent years [1] which provide alternative solutions to the PAPR problem, for example [18, 14, 11, 19, 20, 21, 22, 23, 15, 16, 24, 9, 25, 26, 27, 28, 17, 29]. However, only a few of these have found their way into practical implementations. Some examples of previously proposed solutions, along with their associated limitations are as follows.
1. The introduction of a spectral guard band has the potential of preventing the spectral spillage of high-order non-linear distortion products into adjacent bands and hence mitigates the associated power back-off as well as linearity requirements. However, this approach is spectrally inefficient.
2. The employment of specific coding schemes reducing the PAPR [4,5,6] affects the design of the Forward Error Correction (FEC) coding scheme and hence may degrade the efficiency of the FEC code, as well as reduce the effective throughput, since they introduce redundancy by setting the parity bits of the associated block codes, such that they minimize the PAPR. Moreover, it is not a trivial task to find appropriate PAPR reduction codes for systems having a large number of subcarriers.
3. The set of distortionless techniques proposed in [12,13,14,15,16,17] may increase in importance for employment in future systems, although they exhibit a high complexity.
4. Clipping and filtering the modulated signal [7,8] as well as employing peak windowing [8,9,10,11] can be useful, but may introduce severe in-band distortions of the modulated signal, as now discussed.
The method introduced in [9] proposes to reduce the peak-to-average power ratio of the modulated signals such as OFDM or CDMA by canceling the large signal peaks with the aid of subtracting an appropriately designed reference function. Since the OFDM modulated signal is a composite multicarrier signal, while that of CDMA is a multichip signal, in [9] they were termed as composite-carrier signals. More specifically, the reference function is time shifted and scaled in such a way that after subtracting it from the original signal it reduces the peak power of at least one signal sample. In [9] it was proposed that the reference function should be selected such that its bandwidth was approximately or exactly the same as the bandwidth of the transmitted signal. This assures that the peak-to-average reduction procedure will not impose any out-of-band interference. An example of such a reference function was introduced in [9] which is a sinc function. It can be inferred therefore that the power of the peak cancellation signal is accommodated within the bandwidth of the information-carrying signal, hence causing significant in-band interference. Furthermore, in [9] the peak detection procedure is performed directly after the IFFT stage of the transmitter, resulting in poor peak-capture accuracy.
A technique somewhat similar to that of [9] is proposed in [11] for employment in CDMA-based systems. In [11] the PAPR reduction procedure is performed after oversampling the signal. Furthermore, an error signal is generated first by comparing the original oversampled signal with an amplitude threshold. The resultant error signal is then filtered by a shaping filter, reducing the associated out-of-band emission. Finally, the filtered error signal is subtracted from the original signal for the sake of producing a reduced-PAPR signal. Similarly to [9], the major disadvantage of the method advocated in [11] is that it imposes significant in-band distortion of the resultant signal.
The technique advocated in [17] utilizes one or more frequency tones of a Discrete Multi-Tone (DMT) signal for accommodating a PAPR reducing signal, where the modulating signal was chosen for minimizing the PAPR. In [17] it is proposed to choose the appropriate set of frequency tones for PAPR reduction based on the a posteriori information about the transmission link's frequency-domain transfer function. While this choice of the redundant sub-carriers is attractive, the technique assumes the explicit knowledge of the channel's transfer function at the transmitter, which is not readily available unless it is explicitly signaled by the receiver. Other disadvantages of the approach of [17] will be highlighted later in this section.
The method proposed in [17] was further developed in [15], where the reduction of the peak-to-average power ratio was also achieved by introducing a peak-reduction signal, conveyed by a certain subset of frequencies within the transmitted signal's information carrying bandwidth. An implementation example is provided where a reference function termed as a kernel signal is generated, which accommodates the peak-reduction signal by a specific subset of frequencies. First, similarly to [9] and [11], a time-domain peak detection procedure is invoked. Then the reference function is adjusted and subtracted from the original signal to negate at least one peak sample of the transmitted signal at a time. The PAPR reduction procedure of [15] can be performed iteratively for removing any new peak samples produced during the previous PAPR reduction operation. The appropriate subset of frequencies invoked for accommodating the redundant signal can be chosen randomly, pseudo-randomly or based upon various other criteria, such as the channel's transfer function. The techniques outlined in [15] and [17] have the disadvantage that they impose a certain spectral efficiency degradation, since part of the useful bandwidth is employed for conveying a PAPR reduction signal. Moreover, the methods of [15,17] require the transmission of additional side information about the frequency position of the subcarriers used for accommodating the redundant PAPR-reduction signal. Finally, the techniques of [15,17] are not amenable to employment in the context of the existing family of standardized multi-carrier communication systems, such as the 802.11, or DVB-T systems.
Crest factor reduction was also achieved by applying a correction vector to the transmitted data vector in [18]. The method of calculating the corresponding correction vector is briefly introduced in [18] in the context of OFDM and DMT. However, the method of [18] exhibits significant disadvantages. Specifically, a poor performance is achieved as a consequence of implementing it before oversampling. Furthermore, an in-band signal-to-noise ratio degradation is imposed by the correction vector. Finally, the method of [18] exhibits a high degree of implementation complexity as a result of its iterative nature.